In this video, we will take note of the even subalgebra of G(3), see that it is isomorphic to the quaternions and, in particular, the set of rotors, themselves in the even subalgebra, correspond to the set of unit quaternions. This brings the entire subject of quaternions under the heading of geometric algebra. We will also see that the rotors form a group with the geometric product.
Geometric Algebra playlist: https://www.youtube.com/playlist?list=PLpzmRsG7u_gqaTo_vEseQ7U8KFvtiJY4K
References / Further Reading:
1. Lasenby and Doran's "Geometric Algebra for Physicists". https://www.amazon.com/Geometric-Algebra-Physicists-Chris-Doran/dp/0521715954
2. "A Survey of Geometric Algebra and Geometric Calculus" by Alan Macdonald: http://www.faculty.luther.edu/~macdonal/GA&GC.pdf
3. "Synopsis of Geometric Algebra" and "Geometric Calculus" by David Hestenes: http://geocalc.clas.asu.edu/html/NFMP.html
Note:
1. At 22:15, supposing that i is not equal to j.
Music:
J.S. Bach's Concerto for Two Violins in D minor, 1st Mov.